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CHAPTER-1

CHAPTER-1. Measurements. Chapter 1- Measurement. Topics to be covered : Measurement of a physical parameter Units, systems of units Basic units in mechanics Changing units Significant figures. Ch 1-2 Measuring Things. Units and Standards.

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CHAPTER-1

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  1. CHAPTER-1 Measurements

  2. Chapter 1- Measurement • Topics to be covered : • Measurement of a physical parameter • Units, systems of units • Basic units in mechanics • Changing units • Significant figures

  3. Ch 1-2 Measuring Things • Units and Standards. Measurements of Physical quantity in unit in comparison with a standard. • Each Physical Quantities has its associated unit and a standard to compare with • Base Physical Quantities : Length (L) , Mass (M) and Time (T) • Derived Physical Quantities: speed = length/time acceleration = speed/time force = mass x acceleration

  4. Ch 1-2 Measuring Things • Base Unit associated with base quantities Derived Units associated with derived quantities • Base-Standards associated with base physical quantities Derived-Standards associated with derived quantities • Base Unit Systems International System (mks) Gaussian System (cgs) British engineering system (fps)

  5. Table of Base Units System

  6. Prefix • A multiplier of a unit to increase or decrease its value • Prefix in SI units given in terms of power of tens

  7. Prefix for SI units

  8. Ch 1-4 Changing Units • Changing units using Chain-link conversion Multiplication of original measurement by a conversion factor c • Change of 5 min into seconds Conversion factor c = 60 s/1 min 5 min= 5 min x c = 5 min x (60 s/1 min)=300 s • Conversion factor c for changing year into seconds c =(365 days/1year)x(24 h/1day) x (60 min/ 1 h) x (60 s/1 min)

  9. Significant Figures • Precession in data given by Significant Figures Significant Figures (SF): number of digits in a number, 33 m/s has two digits hence two SF 1.33 m has three SF • Final Result of a calculation cannot be more precise than the least significant figure in the data Z = A(2 SF) x B(3 SF) Z will be rounded off to have 2SF number

  10. Standards -SI units system SI (mks) Unit System Length Mass Time meter (m) kilogram (kg) second (s)

  11. A Earth C Equator B The Meter • In 1792 the meter was defined to be one ten-millionth of the distance from the north pole to the equator. • The meter was later defined as the distance between two fine lines on a standard meter bar made of platinum-iridium. • Since 1983 the meter is defined as the length traveled by light in vacuum during the time interval of 1/299792458 of a second. • The measurement of the speed of light had become extremely precise.

  12. Ch 1-5 Length • SI unit of length-meter Length of a platinum-iridium bar (standard meter bar) kept at International Bureau of Weights and Measures near Paris • The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299792458 of a second: speed of light c =299 792 458 m/s

  13. The Second • Initially the second was defined as follows: • The length of the day is not constant as is shown in the figure. • Since 1967 the second is defined as the time taken by 9192631770 light oscillations of a particular wavelength emitted by a cesium-133 atom. • it would take two cesium clocks 6000 years before their readings would differ by more than 1 second.

  14. Ch 1-6 Time • SI unit of time-second • Time measurement with reference to frequency (9 192 631 770 Hz) of light emitted by cesium-133 atom (atomic clock) • One second is the time taken by 9 192 631 770 oscillations of light emitted by a cesium-133 atom

  15. The Kilogram The SI standard of mass is a platinum-iridium cylinder shown in the figure. The cylinder is kept at the International Bureau of Weights and Measures near Paris and assigned a mass of 1 kilogram. Accurate copies have been sent to other countries.

  16. Ch 1-7 Mass • SI unit of mass-kilogram Mass of a platinum-iridium cylinder (The Standard kilogram) kept at International Bureau of Weights and Measures near Paris. • Second Mass Standard Atomic mass unit (amu): 1 amu = 1.6605402 x 10-27 kg Mass of C-12 atom = 12 amu

  17. Dimensional Analysis • Dimension denotes qualitative nature of a physical quantity • Symbols L, M, T are used to specify length, mass and time nature of a physical quantity respectively. • The brackets [ ] are used to denote the dimension of a physical quantity [velocity v] = L / T ; [Area A] = L2 • Dimensions are treated as algebraic quantities and can be multiplied or divided mutually

  18. Dimensional Analysis • Dimensional Analysis is used to check a formula • A formula is correct only if the dimension of both side of the relationship are same. • Example: Acceleration of a particle moving in a circle is given by : a=krnvm Determine the values of constant k and exponents n and m • The dimensional equation is L/T2=Ln(L/T)m=Ln+m/Tm Equating exponents of L and T separately: 1=n+m; 2=m; m=2; n=1-m=1-2=-1 Then L/T2 = k L/T2 ; and k=1 Hence a=krnvm = r-1v2 = v2/r

  19. Thank you

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